Calculations and Calculators

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Calculations | Mental calculations | Written calculations | Calculators

Calculations

It is important that pupils follow the correct order of operations for arithmetic calculations. Most will be familiar with the mnemonic: BODMAS or BIDMAS.
This shows the order in which calculations should be completed:
  1. Brackets are done first;
  2. then the pOwers or Indices;
  3. Multiplication and Division have equal importance so work left to right;
  4. and finally, Addition and Subtraction - again equal importance so work left to right
Sometimes the mnemonic is better written vertically as:
B
O
DM
AS

Examples

5 + 3 x 4 means
5 + 12 (as multiplication is more important than the addition)= 17 ü
5 + 3 x 4 DOES NOT mean
8 x 4 (the addition was incorrectly completed first)
= 32 x

You could re-write the calculation as:
( 5 + 3 ) x 4 (the brackets are now the most important calculation to do first)
= 8 x 4
= 32

5 + 62 ¸ 3 – 4 (powers calculated first)
= 5 + 36 ¸ 3 – 4 (followed by the division)
= 5 + 12 – 4 (finally the addition and subtraction working from left to right)
= 17 – 4
= 13

Calculations | Mental calculations | Written calculations | Calculators


Mental calculations


Most pupils should be able to carry out the following processes mentally though the speed with which they do it will vary considerably.
  • recall addition and subtraction facts up to 20;
  • recall multiplication and division facts for tables up to 10 x 10.

Pupils should be encouraged to carry out other calculations mentally using a variety of strategies but there will be significant differences in their ability to do so. It is helpful if teachers discuss with pupils how they have made a calculation. Any method which produces the correct answer is acceptable.

eg
53 + 19 = 53 + 20 – 1

284 – 56 = 284 – 60 + 4

32 x 8 = 32 x 2 x 2 x 2

76 ÷ 4 = (76 ÷ 2) ÷ 2


For more details visit the following pages:


Calculations | Mental calculations | Written calculations | Calculators


Written calculations


Pupils often use the ‘ = ‘ sign incorrectly. When doing a series of operations they sometimes write mathematical sentences which are untrue.
eg 5 x 4 = 20 + 3 = 23 – 8 = 15 x since 5 x 4 ≠ 15

It is important that all teachers encourage pupils to write such calculations correctly.
eg 5 x 4 = 20
20 + 3 = 23
23 – 8 = 15 ü

The ‘=‘ sign should only be used when both sides of an operation have the same value. There is no problem with a calculation such as:
43 + 57 = 40 + 3 + 50 + 7 = 90 + 10 = 100 ü since each part of the calculation has the same value.

The ‘≈‘ (approximately equal to) sign should be used when estimating answers.
eg 2 378 – 412 ≈ 2 400 – 400
2 400 – 400 = 2 000 ü

For more details of specific calculation methods visit the following pages:

Calculations | Mental calculations | Written calculations | Calculators


Calculators


Some pupils are over-dependent on the use of calculators for simple calculations. Wherever possible pupils should be encouraged to use mental or pencil and paper methods. It is, however, necessary to give consideration to the ability of the pupil and the objectives of the task in hand. In order to complete a task successfully it may be necessary for pupils to use a calculator for what you perceive to be a relatively simple calculation. This should be allowed if progress within the subject area is to be made. Before completing the calculation pupils should be encouraged to make an estimate of the answer. Having completed the calculation on the calculator they should consider whether the answer is reasonable in the context of the question.

Calculations | Mental calculations | Written calculations | Calculators